Causal Identification under Markov Equivalence: Completeness Results

Abstract

Causal effect identification is the task of determining whether a causal distribution is computable from the combination of an observational distribution and substantive knowledge about the domain under investigation. One of the most studied versions of this problem assumes that knowledge is articulated in the form of a fully known causal diagram, which is arguably a strong assumption in many settings. In this paper, we relax this requirement and consider that the knowledge is articulated in the form of an equivalence class of causal diagrams, in particular, a partial ancestral graph (PAG). This is attractive because a PAG can be learned directly from data, and the scientist does not need to commit to a particular, unique diagram. There are different sufficient conditions for identification in PAGs, but none is complete. We derive a complete algorithm for identification given a PAG. This implies that whenever the causal effect is identifiable, the algorithm returns a valid identification expression; alternatively, it will throw a failure condition, which means that the effect is provably not identifiable. We further provide a graphical characterization of non-identifiability of causal effects in PAGs.

Conference

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Equivalence classes

Bibliographical note

Bareinboim and Jaber are supported in parts by grants from NSF IIS-1704352, IIS1750807 (CAREER), IBM Research,and Adobe Research. Zhang’s research was supported in part by the Research Grants Council of Hong Kong underthe General Research Fund LU13602818.

abstract = "Causal effect identification is the task of determining whether a causal distribution is computable from the combination of an observational distribution and substantive knowledge about the domain under investigation. One of the most studied versions of this problem assumes that knowledge is articulated in the form of a fully known causal diagram, which is arguably a strong assumption in many settings. In this paper, we relax this requirement and consider that the knowledge is articulated in the form of an equivalence class of causal diagrams, in particular, a partial ancestral graph (PAG). This is attractive because a PAG can be learned directly from data, and the scientist does not need to commit to a particular, unique diagram. There are different sufficient conditions for identification in PAGs, but none is complete. We derive a complete algorithm for identification given a PAG. This implies that whenever the causal effect is identifiable, the algorithm returns a valid identification expression; alternatively, it will throw a failure condition, which means that the effect is provably not identifiable. We further provide a graphical characterization of non-identifiability of causal effects in PAGs.",

author = "Amin JABER and Jiji ZHANG and Elias Bareinboim",

note = "Bareinboim and Jaber are supported in parts by grants from NSF IIS-1704352, IIS1750807 (CAREER), IBM Research, and Adobe Research. Zhang’s research was supported in part by the Research Grants Council of Hong Kong under the General Research Fund LU13602818.",

year = "2019",

month = "6",

language = "English",

series = "Proceedings of Machine Learning Research (PMLR)",

pages = "2981--2989",

editor = "Kamalika Chaudhuri and Ruslan Salakhutdinov",

booktitle = "Proceedings of the 36th International Conference on Machine Learning",

N1 - Bareinboim and Jaber are supported in parts by grants from NSF IIS-1704352, IIS1750807 (CAREER), IBM Research,
and Adobe Research. Zhang’s research was supported in part by the Research Grants Council of Hong Kong under
the General Research Fund LU13602818.

PY - 2019/6

Y1 - 2019/6

N2 - Causal effect identification is the task of determining whether a causal distribution is computable from the combination of an observational distribution and substantive knowledge about the domain under investigation. One of the most studied versions of this problem assumes that knowledge is articulated in the form of a fully known causal diagram, which is arguably a strong assumption in many settings. In this paper, we relax this requirement and consider that the knowledge is articulated in the form of an equivalence class of causal diagrams, in particular, a partial ancestral graph (PAG). This is attractive because a PAG can be learned directly from data, and the scientist does not need to commit to a particular, unique diagram. There are different sufficient conditions for identification in PAGs, but none is complete. We derive a complete algorithm for identification given a PAG. This implies that whenever the causal effect is identifiable, the algorithm returns a valid identification expression; alternatively, it will throw a failure condition, which means that the effect is provably not identifiable. We further provide a graphical characterization of non-identifiability of causal effects in PAGs.

AB - Causal effect identification is the task of determining whether a causal distribution is computable from the combination of an observational distribution and substantive knowledge about the domain under investigation. One of the most studied versions of this problem assumes that knowledge is articulated in the form of a fully known causal diagram, which is arguably a strong assumption in many settings. In this paper, we relax this requirement and consider that the knowledge is articulated in the form of an equivalence class of causal diagrams, in particular, a partial ancestral graph (PAG). This is attractive because a PAG can be learned directly from data, and the scientist does not need to commit to a particular, unique diagram. There are different sufficient conditions for identification in PAGs, but none is complete. We derive a complete algorithm for identification given a PAG. This implies that whenever the causal effect is identifiable, the algorithm returns a valid identification expression; alternatively, it will throw a failure condition, which means that the effect is provably not identifiable. We further provide a graphical characterization of non-identifiability of causal effects in PAGs.

UR - http://proceedings.mlr.press/v97/jaber19a.html

M3 - Conference paper (refereed)

T3 - Proceedings of Machine Learning Research (PMLR)

SP - 2981

EP - 2989

BT - Proceedings of the 36th International Conference on Machine Learning